{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:JMAMD3LYIVUYVC2PYT2GV2KL7Q","short_pith_number":"pith:JMAMD3LY","schema_version":"1.0","canonical_sha256":"4b00c1ed7845698a8b4fc4f46ae94bfc052b4d2c306fae729497c52392e06dda","source":{"kind":"arxiv","id":"1609.05843","version":2},"attestation_state":"computed","paper":{"title":"Limiting distribution of eigenvalues in the large sieve matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Florin P. Boca, Maksym Radziwi{\\l}{\\l}","submitted_at":"2016-09-19T18:11:56Z","abstract_excerpt":"The large sieve inequality is equivalent to the bound $\\lambda_1 \\leqslant N + Q^2-1$ for the largest eigenvalue $\\lambda_1$ of the $N$ by $N$ matrix $A^{\\star} A$, naturally associated to the positive definite quadratic form arising in the inequality. For arithmetic applications the most interesting range is $N \\asymp Q^2$. Based on his numerical data Ramar\\'e conjectured that when $N \\sim \\alpha Q^2$ as $Q \\rightarrow \\infty$ for some finite positive constant $\\alpha$, the limiting distribution of the eigenvalues of $A^{\\star} A$, scaled by $1/N$, exists and is non-degenerate.\n  In this pape"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1609.05843","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-19T18:11:56Z","cross_cats_sorted":[],"title_canon_sha256":"3f00e79871da3a11173287c166268872be3a67b9b348be099ce1ff3f437f8ea9","abstract_canon_sha256":"cf6b6461099ff978e7097ac4cc979bf4abaa0184b14445b3fc9217cdd76b4f88"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:13.647697Z","signature_b64":"BjNLtbyBQfiUBBF2GnsL3LdTLsYwd+Ysm0NxRFqKoA9EwdQ7ZznotM0VXAsvy+VqFhjmbs1Wna7PCOQ5BPFMDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b00c1ed7845698a8b4fc4f46ae94bfc052b4d2c306fae729497c52392e06dda","last_reissued_at":"2026-05-18T00:13:13.646915Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:13.646915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Limiting distribution of eigenvalues in the large sieve matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Florin P. Boca, Maksym Radziwi{\\l}{\\l}","submitted_at":"2016-09-19T18:11:56Z","abstract_excerpt":"The large sieve inequality is equivalent to the bound $\\lambda_1 \\leqslant N + Q^2-1$ for the largest eigenvalue $\\lambda_1$ of the $N$ by $N$ matrix $A^{\\star} A$, naturally associated to the positive definite quadratic form arising in the inequality. For arithmetic applications the most interesting range is $N \\asymp Q^2$. Based on his numerical data Ramar\\'e conjectured that when $N \\sim \\alpha Q^2$ as $Q \\rightarrow \\infty$ for some finite positive constant $\\alpha$, the limiting distribution of the eigenvalues of $A^{\\star} A$, scaled by $1/N$, exists and is non-degenerate.\n  In this pape"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05843","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1609.05843","created_at":"2026-05-18T00:13:13.647050+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.05843v2","created_at":"2026-05-18T00:13:13.647050+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.05843","created_at":"2026-05-18T00:13:13.647050+00:00"},{"alias_kind":"pith_short_12","alias_value":"JMAMD3LYIVUY","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"JMAMD3LYIVUYVC2P","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"JMAMD3LY","created_at":"2026-05-18T12:30:25.849896+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JMAMD3LYIVUYVC2PYT2GV2KL7Q","json":"https://pith.science/pith/JMAMD3LYIVUYVC2PYT2GV2KL7Q.json","graph_json":"https://pith.science/api/pith-number/JMAMD3LYIVUYVC2PYT2GV2KL7Q/graph.json","events_json":"https://pith.science/api/pith-number/JMAMD3LYIVUYVC2PYT2GV2KL7Q/events.json","paper":"https://pith.science/paper/JMAMD3LY"},"agent_actions":{"view_html":"https://pith.science/pith/JMAMD3LYIVUYVC2PYT2GV2KL7Q","download_json":"https://pith.science/pith/JMAMD3LYIVUYVC2PYT2GV2KL7Q.json","view_paper":"https://pith.science/paper/JMAMD3LY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.05843&json=true","fetch_graph":"https://pith.science/api/pith-number/JMAMD3LYIVUYVC2PYT2GV2KL7Q/graph.json","fetch_events":"https://pith.science/api/pith-number/JMAMD3LYIVUYVC2PYT2GV2KL7Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JMAMD3LYIVUYVC2PYT2GV2KL7Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JMAMD3LYIVUYVC2PYT2GV2KL7Q/action/storage_attestation","attest_author":"https://pith.science/pith/JMAMD3LYIVUYVC2PYT2GV2KL7Q/action/author_attestation","sign_citation":"https://pith.science/pith/JMAMD3LYIVUYVC2PYT2GV2KL7Q/action/citation_signature","submit_replication":"https://pith.science/pith/JMAMD3LYIVUYVC2PYT2GV2KL7Q/action/replication_record"}},"created_at":"2026-05-18T00:13:13.647050+00:00","updated_at":"2026-05-18T00:13:13.647050+00:00"}